An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure

The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg's uncertainty relation and Schrodinger's uncertainty relation. In this paper, we prove a Schrodinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, U-rho((g, f))(A)U-rho((g, f))(B) >= f(0)(2)l/k vertical bar Corr(rho)(s(g,f))(A, B)vertical bar(2) for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix rho. As applications, we derive some new uncertainty relations for Wigner-Yanase skew information and Wigner-Yanase-Dyson skew information.